StatReason

Levene Variance Test

Test whether two or more independent groups show evidence of different variance, before deciding which comparison method fits your data.

One group per line, comma-separated values. At least 2 groups required.

What this answers

This test answers "do these groups show evidence of different amounts of variability, not just different averages?" It is commonly run before an ANOVA or t-test to check whether the equal-variance assumption behind some versions of those tests looks reasonable for your data.

How it is calculated

This calculator uses the Brown-Forsythe variant by default, centering each group on its own median rather than its mean before comparing absolute deviations, which makes the test more robust to skewed data than the classic mean-centered Levene test. Concretely, it computes each observation's absolute distance from its own group's median, then runs a standard one-way ANOVA F-test on those distances across groups. A large W statistic means the average distance from center differs meaningfully across groups.

Worked example

For a tightly clustered group (1, 2, 3, 4, 5) compared against a group that swings widely (1, 10, 1, 10, 1): the second group's absolute deviations from its own median are far larger and more variable than the first group's, producing a large W statistic and strong evidence of unequal variance between the two groups.

Assumption audit

Calculated from your data: each group's median (the centering point), the resulting absolute deviations, and the W statistic built from them.
Evidence to review: the W statistic and p-value here are evidence about variance equality, not a pass/fail gate. A nonsignificant result does not prove the variances are exactly equal, only that this data did not provide strong evidence they differ.
You must verify: that your groups are independent, and that any decision about which downstream test to use (pooled versus Welch, for example) considers this result as one input, not an automatic switch.

What this result does not mean

A significant result here means the data provide evidence the groups' variances differ, it does not by itself mean the groups' means differ; that is a separate question answered by a group-comparison test. A nonsignificant result does not prove the variances are equal, only that this specific test found no strong evidence of a difference.

Limitations

This test's own power depends on sample size, like any statistical test; with small groups, even a real difference in variance may not reach significance. Because this site's t-tests already default to the variance-robust Welch method, this test is most useful as a diagnostic check, not a required gate before every comparison.